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Ch 6.3 General Probability Rules

Ch 6.3 General Probability Rules. AP STATISTICS. Types of Probability. Theoretical: true mathematical probability Empirical: the relative frequency with which an event occurs in a given experiment Subjective: an educated guess. Review Terms.

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Ch 6.3 General Probability Rules

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  1. Ch 6.3 General Probability Rules AP STATISTICS

  2. Types of Probability • Theoretical: true mathematical probability • Empirical: the relative frequency with which an event occurs in a given experiment • Subjective: an educated guess

  3. Review Terms • Experiment: any process that yields a result or observation • Outcome: a particular result of an experiment • Sample Space: the collection of all possible outcomes • Event: any collection of outcomes; any subset of the sample space • Example: Roll die • Let A={1} • Let B={2, 4, 6} • Let C={3, 6} • An event occurs if any outcome of the event occurs

  4. Probability of Event • P(A) = # of outcomes/# outcomes in sample space • If each outcome is equally likely • Using previous slide’s events: • P(A)= • P(B)= • P(C)=

  5. Rules of Probability • Rule 1: For any event, • Rule 2: Complement Rule • “A complement” is the event that A does not occur; the set of all outcomes not in A • Example: even/odd; alive/dead • P(ACE)= • P(ACE’)=

  6. Rules of Probability • Rule 3: Mutually Exclusive/disjoint-two events, A & B that have no outcomes in common • Examples: red and spade; freshman, sophomore, junior • Note: complementarymutually exclusive ; mutually exclusivecomplementary • Rule 4: Additive Rule for disjoint events • Example: P(red or spade)=P(red) + P(spade)=

  7. Rules of Probability • Rule 5: Additive Rule-For any events A & B, P(A or B)=P(A)+P(B)-P(A and B) Example: Find the probability of drawing red card or Ace. • Rule 6: Conditional Probability-For two events A and B, the probability that A occurs given that B has occurred.

  8. Probability Rules • Example: What is the probability that a card is a diamond, given that it is red? • Example: What is the probability of 2, given that you got an even number?

  9. Independent Events • 2 events A and B are independent if the occurrence of one event doesn’t affect the probability of occurrence of the other event • To prove: • Example: rolling two dice; drawing from a deck with replacement • Are drawing a face card and drawing a red card independent events? So they are independent.

  10. Probability Rules • Rule 7: Multiplicative Rule for Independent Events- • Has to be shown or given • Example: Find the probability of drawing two Queens from a deck of cards if it is done with replacement. • Rule 8: Multiplicative Rule- For any two events A& B, the or • Example: Find the probability of drawing two Queens from a deck of cards if it is done without replacement

  11. Example: Contingency Table • P(1990’s)= • P(PG-13)= • P(1990s and PG-13)= • Are 1990s and PG-13 disjoint events?

  12. The probability that a randomly selected DVD is rated PG-13 or is from the 1990s. • P(PG-13 or 1990s)=P(PG13)+P(90s)-P(PG13 and 90s) =.58+.18-.14=.62 • Are PG-13 and 1990s independent or dependent events? dependent Other ways:

  13. Homework • 6.69, 71, 78 Have a wonderful weekend!

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